Landslide displacement prediction from on-site deformation data based on time series ARIMA model

Abstract

Time series Autoregressive Integrated Moving Average (ARIMA) model is often used in landslide prediction and forecasting. However, few conditions have been suggested for the application of ARIMA models in landslide displacement prediction. This paper summarizes the distribution law of the tangential angle in different time periods and analyzes the landslide displacement data by combining wavelet transform. It proposes an applicable condition for the ARIMA model in the field of landslide prediction: when the landslide deformation is in the initial deformation to initial acceleration stage, i.e., the tangential angle of landslide displacement is less than 80°, the ARIMA model has higher prediction accuracy for 24-h landslide displacement data. The prediction results are RMSE = 4.52 mm and MAPE = 2.39%, and the prediction error increases gradually with time. Meanwhile, the ARIMA model was used to predict the 24-h displacements from initial deformation to initial acceleration deformation for the landslide in Guangna Township and the landslide in Libian Gully, and the prediction results were RMSE = 1.24 mm, MAPE = 1.34% and RMSE = 5.43 mm, MAPE = 1.67%, which still maintained high accuracy and thus verified this applicable condition. At the same time, taking the landslide of Libian Gully as an example, the ARIMA model was used to test the displacement prediction effect of the landslide in the Medium-term acceleration stage and the Imminent sliding stage (the tangential angle of landslide displacement is 80° and 85°, respectively). The relative error of displacement data prediction in the Medium-term acceleration stage is within 3%, while the relative error of the prediction value in the Imminent sliding stage is more than 3%, and the error gradually increases with time. This demonstrates that the relative error of the ARIMA model in landslide prediction and forecasting is within 3%. The relative error of the prediction value in the Imminent sliding stage is above 3%, and the error increases gradually with time. Meanwhile, the prediction results are analyzed and it is concluded that the increase in prediction time and tangential angles are the main reasons for the increase in error. The applicable conditions proposed in this study can provide a reference for the application of ARIMA model in landslide prediction and forecast.